Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
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In this lecture we study the nonlinear <strong>Dirichlet</strong> problem<br />
� Δu + f (u) = 0 in Ω,<br />
u = 0 on ∂Ω,<br />
where Δ is the Laplacian operator, Ω ⊂ R N is a bounded region with<br />
MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 3➲<br />
▲ ▲<br />
(0.1)<br />
smooth boundary, and f : R → R is a function of class C 1 asymptotically<br />
linear, i.e.<br />
.<br />
f ′ (∞) := lím<br />
|t|→∞ f ′ (t) ∈ R.<br />
➲ ❏ ✘